Design-Based Confidence Sequences: A General Approach to Risk Mitigation in Online Experimentation

TL;DR

This paper introduces a general method for constructing valid confidence sequences in online experiments, enabling risk mitigation and early stopping without invalidating statistical guarantees.

Contribution

It provides a novel, assumption-light framework for confidence sequences applicable to various experimental designs, including multi-arm bandits and time series, with variance reduction techniques.

Findings

Confidence sequences control type-1 error over time

Early stopping can be achieved after few observations

Real-world Netflix experiments demonstrate practical effectiveness

Abstract

Randomized experiments have become the standard method for companies to evaluate the performance of new products or services. In addition to augmenting managers' decision-making, experimentation mitigates risk by limiting the proportion of customers exposed to innovation. Since many experiments are on customers arriving sequentially, a potential solution is to allow managers to "peek" at the results when new data becomes available and stop the test if the results are statistically significant. Unfortunately, peeking invalidates the statistical guarantees for standard statistical analysis and leads to uncontrolled type-1 error. Our paper provides valid design-based confidence sequences, sequences of confidence intervals with uniform type-1 error guarantees over time for various sequential experiments in an assumption-light manner. In particular, we focus on finite-sample estimands defined on the study participants as a direct measure of the incurred risks by companies. Our proposed confidence sequences are valid for a large class of experiments, including multi-arm bandits, time series, and panel experiments. We further provide a variance reduction technique incorporating modeling assumptions and covariates. Finally, we demonstrate the effectiveness of our proposed approach through a simulation study and three real-world applications from Netflix. Our results show that by using our confidence sequence, harmful experiments could be stopped after only observing a handful of units; for instance, an experiment that Netflix ran on its sign-up page on 30,000 potential customers would have been stopped by our method on the first day before 100 observations.